AUSTIN, Texas (AP) -- Texas is holding the nation's first primary election Tuesday with a political free-for-all in Republican races that could push the state further right, though Democrats are calling it the next big electoral battleground.

Republican Gov. Rick Perry has decided this would be his last of a record 14 years in office, and his looming exit has set off a scramble resulting in the most open races in Texas in more than a decade.

Republicans are favored to win them all come November - including Perry's seat, despite Democrat Wendy Davis building a national profile and an early $16 million fundraising haul to match. She has energized Texas Democrats, who haven't won a statewide race in 20 years but insist the tide is turning.

That possibility, and the rising influence of tea party firebrand U.S. Sen. Ted Cruz, has Texas Republicans flanking farther right this primary season. Some blasted an "invasion" of immigrants coming across the Texas border, where immigration arrests have almost tripled in recent years but remain at about one third of their historic highs. Others pledged to further tighten some of the nation's strictest abortion laws and doubled down on the state's gay marriage ban - one of several state bans recently ruled unconstitutional by federal courts.

And a new member of the Bush dynasty is on the ballot: George P. Bush, the nephew of former President George W. Bush and son of former Gov. Jeb Bush, is making his political debut by running for land commissioner. On the eve of Tuesday's primary, the younger Bush - who is widely considered a future Texas GOP leader - told voters the biggest opponent this year is President Barack Obama.

"This is a call to look out for the next generation of Texans," he said at a Monday campaign stop in El Paso. "I want to continue to fight the good fight."

Frigid weather greeted some voters with a dangerous drive to the polls. Polling locations around Austin were opening on a four-hour delay because of icy conditions, and state elections officials urged counties to plan for alternatives in case some sites can't open.

Six of Texas' top offices lack an incumbent; the last time Texas had so many open statewide seats was 2002, when Perry won his first full term. While Democrats are running mostly unopposed in their primaries, crowded fields in the Republican races for attorney general, comptroller and commissioners for agriculture and railroads make May runoffs likely.

Davis' bid for governor headlines a roster of underdog Democrats girding instead for the Nov. 4 general election.

That's the only day that matters to Davis and her Republican opponent, Attorney General Greg Abbott, in the year's marquee showdown. Neither has a competitive primary, leaving Davis poised to become the first female gubernatorial nominee in Texas since Ann Richards in 1994, and Abbott the first new GOP nominee since Perry.

Unlike Davis and Abbott, few other Texas candidates have the luxury of uneventful primaries.

Almost all are on the Republican side, where candidates have wooed voters with vows to emulate Cruz's no-compromise style. Even U.S. Sen. John Cornyn and U.S. Rep. Pete Sessions, two of the state's most powerful Republicans, have spent money campaigning against longshot challengers who say the incumbents have grown too moderate in Washington.

Changes are far more likely in Austin. Republican Lt. Gov. David Dewhurst, who lost to Cruz in the U.S. Senate race in 2012, appears headed for his first runoff in 11 years on the job. The race has been the nastiest and most competitive this primary season.

"When there's a fair amount of negative out there it makes the electorate very unpredictable," said Land Commissioner Jerry Patterson, one of four Republicans vying for the state's No. 2 job, which doubles as the state Senate president and exerts considerably more influence than in other states in setting the legislative agenda.

Marian Price said that race brought her out to cast a Republican ballot in Dallas. The 56-year-old legal secretary said she would vote for Dewhurst's "centrist" approach, but criticized all four lieutenant governor candidates for their response to the case of a pregnant, brain-dead Texas woman whose family had to fight in court to have her taken off life support.

The candidates argued state law needed to be modified to keep the woman alive and ensure her fetus survived. Price said they were promoting an unnecessary government intrusion into a private family decision, one example of how she said the tea party is pushing Republicans too far.

"I'm not voting for anyone Ted Cruz supports," said Price, saying she now considers herself more of an independent.

Illinois holds the nation's next primary March 18, followed by a flood of state primaries in May and June.

A blustery winter storm dumped snow and ice across the West on Wednesday, making driving treacherous in the mountains from California to the Rockies and forcing residents and party-goers in some usually sun-soaked cities to bundle up for a frosty New Year's.

House Republican leaders rallied around one of their own, Whip Steve Scalise, on Tuesday after he said he regrets speaking 12 years ago to a white supremacist organization and condemns the views of such groups.

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